NJSLA Geometric Principles and Measurement 4 — Questions and Answers
Question 1: An exterior angle of a triangle measures 130°. One of the non-adjacent interior angles measures 75°. What is the other non-adjacent interior angle?
- 45°
- 50°
- 55° (Correct answer)
- 60°
Correct answer: 55°
An exterior angle equals the sum of the two non-adjacent interior angles: 130° = 75° + x, so x = 55°.
Question 2: A rectangular prism has dimensions 4 cm × 6 cm × 9 cm. What is its total surface area?
- 216 cm²
- 228 cm² (Correct answer)
- 264 cm²
- 312 cm²
Correct answer: 228 cm²
SA = 2(lw + lh + wh) = 2(24 + 36 + 54) = 2(114) = 228 cm².
Question 3: Point M is the midpoint of segment PQ. P is at (−4, 2) and M is at (1, 5). What are the coordinates of Q?
- (6, 8) (Correct answer)
- (3, 7)
- (−1, 3.5)
- (2, 4)
Correct answer: (6, 8)
Using midpoint formula: 1 = (−4 + x)/2 → x = 6; 5 = (2 + y)/2 → y = 8, so Q = (6, 8).
Question 4: Two supplementary angles are in the ratio 2:7. What are their measures?
- 20° and 70°
- 36° and 126°
- 40° and 140° (Correct answer)
- 45° and 135°
Correct answer: 40° and 140°
2x + 7x = 180°, so 9x = 180°, x = 20°; the angles are 40° and 140°.
Question 5: A sphere has a diameter of 12 cm. What is its volume? (Use π ≈ 3.14)
- 904.32 cm³ (Correct answer)
- 2143.57 cm³
- 1809.6 cm³
- 7234.56 cm³
Correct answer: 904.32 cm³
Radius = 6 cm; V = (4/3)πr³ = (4/3)(3.14)(216) = 904.32 cm³.
Question 6: Which quadrilateral always has diagonals that are perpendicular bisectors of each other?
- Rectangle
- Parallelogram
- Rhombus (Correct answer)
- Trapezoid
Correct answer: Rhombus
In a rhombus, the diagonals are always perpendicular bisectors of each other.
Question 7: A scale drawing uses a scale of 1 inch : 15 feet. If a room measures 3.5 inches on the drawing, what is its actual length?
- 45 feet
- 50 feet
- 52.5 feet (Correct answer)
- 60 feet
Correct answer: 52.5 feet
Actual length = 3.5 × 15 = 52.5 feet.
NJSLA Geometric Principles and Measurement 4
An exterior angle of a triangle measures 130°.
One of the non-adjacent interior angles measures 75°.
What is the other non-adjacent interior angle?